According to modal realism, logical space consists of concrete possible worlds that are spatiotemporally and causally isolated from each other. The aim of the paper is to show that modal realism may not be able to accomplish some of its explanatory tasks because it cannot warrant that logical space is sufficiently diverse. In particular, it cannot exclude the possibility that merely possible worlds are indistinguishable from the actual world in certain important respects. If this is the case, modal realism cannot explain the truth of some modal statements that are obviously true or the contingency of some non-modal statements that are obviously ontingent